The present invention relates to a time-series prediction method and apparatus utilizing wavelet coefficient series.
Conventionally, time-series prediction has been performed in solely the time domain or in solely the frequency domain. Time-domain prediction is performed as shown in FIG. 1, and many models, such as a linear regression model, pertain to time-domain prediction. Frequency-domain prediction is performed as shown in FIG. 2, and a model for inferring the shape of a power spectrum pertains to frequency-domain prediction. These traditional methods have been studied widely and applied to actual time-series prediction.
However, in the above-described conventional methods, prediction accuracy decreases for a time series having a certain time configuration in solely a specific frequency band or for a composite time series having a different time configuration in each of different frequency bands. This is because prediction in solely the time domain or in solely the frequency domain cannot simultaneously handle information in the time domain and information in the frequency domain.
Incidentally, when a time series is subjected to wavelet expansion, the time series is represented in the form of the sum of frequency components localized in the time domain.
In view of the foregoing, an object of the present invention is to provide a time-series prediction method and apparatus utilizing wavelet coefficient series which can obtain a prediction value of an original time series through an operation of wavelet-transforming the time series to thereby decompose the time series into a plurality of time series which are band-restricted in the frequency domain, and then inversely transforming the individual prediction values of the plurality of time series of the respective frequency components.
To achieve the above object, the present invention provides the following.
[1] A time-series prediction method utilizing wavelet coefficient series comprising: (a) wavelet-transforming a time series by use of a wavelet transformation unit in order to decompose the time series into a plurality of time series which are band-restricted in the frequency domain; (b) predicting values of frequency components obtained as a result of decomposition, by use of corresponding prediction units; and (c) reconstructing the prediction values of the respective frequency components by use of an inverse wavelet transformation unit to thereby obtain a prediction value of the original time series.
[2] A time-series prediction method utilizing wavelet coefficient series as described in [1] above, characterized in that ordinary wavelet transformation is used in order to wavelet-transform the time series to thereby univocally decompose the time series into a plurality of time series of the respective frequency components.
[3] A time-series prediction method utilizing wavelet coefficient series as described in [1] above, characterized in that stationary wavelet transformation is used for decomposition of the time series in order to observe the frequency components of the time series while aligning their observation times.
[4] A time-series prediction apparatus utilizing wavelet coefficient series, comprising: (a) a wavelet transformation unit for decomposing a time series into a plurality of coefficient series of different frequency components; (b) prediction units for predicting values of the respective frequency components; and (c) an inverse wavelet transformation unit for reconstructing the prediction values of the respective frequency components to thereby obtain a prediction value of the original time series.